Volume 15 Number 4 ISSN 1074-3197 (printed) ISSN 1074-8059 (digital) December 2008 Journal of the North American Sundial Society The Compendium* Photo by Rudy Light The eye is always caught by light, but shadows have more to say…. - Gregory Maguire (Mirror-Mirror) * Compendium... "giving the sense and substance of the topic within small compass." In dialing, a compendium is a single instrument incorporating a variety of dial types and ancillary tools. © 2008 North American Sundial Society NASS Officers President & Editor: Frederick W. Sawyer III Vice President: Don Petrie 8 Sachem Drive, Glastonbury, CT 06033 462 Millard Street, Stouffville, ON L4A 8A8 Canada [email protected] [email protected] Secretary: Roger T. Bailey Treasurer: Robert L. Kellogg 10158 Fifth Street, Sidney, BC V8L 2Y1 Canada 10629 Rock Run Drive, Potomac, MD 20854 [email protected] [email protected] Annual membership in the North American Sundial Society includes 4 issues of The Compendium. The Compendium is published in both print and digital editions; the digital edition (in pdf format) may be received either on CD or by Internet download. To join NASS, contact Fred Sawyer at the above address. North Elsewhere – by Air Mail America (US Dollars or GB Pounds (US Dollars) incl. postage) 1 Yr. 2 Yr. 1 Yr. 2 Yr. 1Yr. 2 Yr. Membership & Print edition of Compendium $30 $57 $45 $86 £26 £50 Membership & Digital Compendium on CD $25 $48 $35 $67 £20 £39 Membership & Digital Compendium by download $20 $38 $20 $38 £12 £23 Membership with both Print & CD editions $42 $80 $57 $108 £33 £63 Membership with both Print & download editions $35 $67 $50 $95 £29 £55 The North American Sundial Society, Inc. is a not-for-profit 501(c)3 educational organization incorporated in the state of Maryland. IRS Form-990, supporting financial statements, and exemption information are available from the NASS Treasurer upon letter or email request to nass- [email protected]. Contents Sundials for Starters – Azimuth Of Sunrise Robert L. Kellogg 1 Lines For Unequal Hours Are Not Straight Alessandro Gunella 6 Sheldon Moore’s Sundial Business Conn. Historical Society 7 A Triple Horizontal Sundial For California John Davis 11 Gnomonics In A Japanese Jr. High School Entrance Exam Barry Duell 22 Sightings… In Carnegie Steven R. Woodbury 23 A Shadow Plane Hours-Until-Sunset Dial Mac Oglesby 24 Slope Of The Summer Solstice Curve At Large Hour Angles Ortwin Feustel 28 Quiz Answer: Ancient Sundial Location Posed by Ortwin Feustel 33 A Glimpse Of Alsace Fred Sawyer 34 Quiz: Nicole’s Reflections Fred Sawyer 38 The Tove’s Nest 39 Digital Bonus 40 Sundials for Starters – Azimuth Of Sunrise Robert L. Kellogg (Potomac MD) Archeology at Stonehenge is the cover story in the June 2008 issue of the National Geographic. Located 6 miles north of Salisbury, England on a grassy plain are the famous linteled monoliths (Fig. 1). In the United States and Canada there are interesting, but less famous, solar alignments called “Medicine Circles” and “Sun-Circles” to sight the equinoxes and solstices. In the U.S. the largest sun-circle is the Cahokia Woodhenge located about 8 miles across the Mississippi river from St. Louis near Collinsville, Illinois. The Wood- henge is part of Cahokia Mounds Historic State Park that has been designated by UNESCO as a World Heritage Site. Within Figure1. Stonehenge the nearly six square miles are over 120 earthwork mounds built by the Mississippian Indians. The largest is Monks’ Mound measuring 100 (30.5m) feet tall and nearly 1000 feet (305m) long. The Mississippians also constructed earthworks in Mississippi (Ocmulgee Mound) and Ohio (Serpent Mound). Figure 2. Cahokia Woodhenge Site Map ! The Compendium - Volume 15 Number 4 December 2008 Page 1 Excavations at the Cahokia began in the 1920’s, but it was Robert Hill, William Iseminger and Warren Wittry who discovered large “bathtub” pits in the early 1960’s. They called them bathtub pits because of their similarity in shape to an old-time bathtub. The effect was caused by a ramp dug from the ground to the bottom of the pit, and it is associated with the job of erecting a tall wooden pole into the pit. While many of the ordinary pits are randomly placed, the bathtub pits are uniformly placed along circular arcs. According to Michael W. Friedlander1 “The first recognition of layout around circles and possible astronomical attributes was seen by Wittry2” Several circles were discovered, with the most complete circle named by the archaeologists as Circle #2. The western edge of the Circle #2 archeological site (Tract 15-1A) was destroyed in the early 1960’s by the construction of a highway gravel pit (Fig. 2). Only 39 pits of what would have been a 48 wood post circle remain, but their positions were done with extreme care. The posts were accurately placed within 15 inches (38 cm) along a uniform circle 205 feet (62.5m) in radius. In 1985 wooden posts were erected at the excavated bathtub pits to give a sense of the size and shape of the Cahokia Woodhenge (Fig. 3). But how were they used? Let’s become astro-archaeological detectives. Figure 3. Cahokia Woodhenge The north, east and south posts are nearly perfectly aligned with the cardinal points. The west post position was destroyed by the 1960’s gravel pit. From the center of the circle, the azimuth of each post is almost exactly 7.5o. According to Friedlander, “The distance was calculated to each post-hole, yielding a mean value for the circle radius R=205.0 +/- 0.7 ft.”; and “the actual average spacing, derived from Wittry’s post-hole locations is 7.51o +/-0.35o”. Near the center of the sun-circle Wittry found another bathtub pit. But instead of being in the exact center of the sun-circle, it was located east of center by 5 ¾ feet (1.75m). Standing at this post (the “observation 1 Friedlander, Michael W. “The Cahokia Sun-Circles”, The Wisconsin Archeologist, Vol. 88(1), pp.78-90, 2007. 2 Wittry, Warren “An American Woodhenge”, Cranbrook Institute of Science Newsletters, Vol. 33(9), pp. 102-107, 1964 Bloomfield Hills, Michigan. Reprinted in Explorations into Cahokia Archaeology, Bulletin 7, Illinois Archaeological Survey, 1969. ! The Compendium - Volume 15 Number 4 December 2008 Page 2 post”) the apparent azimuth of the circle of posts is changed ever so slightly. We’ll concentrate on two posts that seem to be related to the solstices: post #8 and post #16, with azimuths given in Table 1 below. As astro-archaeologists we can compare these azimuths to the sunrise summer and winter solstices and check for an alignment. We will start with the standard sundialist’s equation of azimuth: sin(lat )cos( z )− sin( dec ) cos(180−Az ) = − (1) cos(lat )sin( z ) where Az = sun’s azimuth measured clockwise from north lat = site latitude dec = declination of the sun (see more below about this) z = solar zenith angle We also have a relationship between zenith angle and the sun’s hour angle HA, (the longitude from local meridian) as: cos(z) = sin(lat)sin(dec)+cos(lat)cos(dec)cos(HA) (2) cos(z )− sin( lat )sin( dec ) or cos(HA ) = (3) cos(lat )cos( dec ) To use these equations, we need to find the solar declination at the solstices 1000 years ago. We know that today this value (also called the earth’s obliquity, “ε”) is 23.4383o. The obliquity is the sun’s declination on the solstices: summer uses +ε while winter uses -ε. But we need the obliquity for 1000 CE. 1000 years ago the obliquity was 23.569o, derived from an approximate equation to account for earth precession effects: ε =23o + 0.43929111+T( − 46.815 + T( − .00059 + T(.001813)))/3600 (4) where T = number of centuries from the 2000. Ignoring refraction, the sundialist’s sunrise occurs exactly on the horizon for the center of the sun. This means that the zenith angle z=90o. Finally, the only other piece of information we need is Cahokia’s latitude of 36.86599o. We then solve equation (1) for the sun’s azimuth and add that to our Table 1 set of information: Circle Center Observer Post Horizon Sunrise at Post Azimuth Azimuth Solstice 1000 CE Post #8 60.02 o 59.12 o 58.42 o Post #16 121.01 o 121.77 o 120.03 o Table 1 Azimuths from Center of Sun-Circle and from Observer Post These results at first look very promising. Whether it be from the center of the sun-circle or the observer’s post, the angles match that of a simple solstice sunrise within a couple of degrees. Our euphoria at becoming the next Indiana Jones is shattered however when we realize that (1) we have ignored refraction, (2) we’ve used the center of the sun and may need to use the upper or bottom limb of the sun as a realistic, observable marker, and (3) we have ignored the Collinsville Bluffs that rise above the true horizon. The bluffs are only about 120 feet (36.5m) high, but run at an angle to the sun-circle such that they are at a distance of 23800 feet (7.25 km) in the direction of post #8 and 16750 feet (5.1 km) in the direction of post #16 [from Friedlander reporting on various investigations], giving Summer Apparent Horizon = ToDeg*ATAN(120/23800) = 0.29o (5) ! The Compendium - Volume 15 Number 4 December 2008 Page 3 Winter Apparent Horizon = ToDeg*ATAN(120/16750) = 0.41o (6) (Remember that many spreadsheet formulas need conversions into degrees => pi/180° or into radians => 180°/pi.) Refraction is perhaps the hardest thing to handle.